The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.

eng

dc.description

Title from title screen of research.pdf file (viewed on October 9, 2007)

The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for the [xi]-index, a spectral parameter independent counterpart of Krein's spectral shift function. The proofs of the main results are based on diverse properties of the operator logarithm and argument averaged with respect to a normal tracial state that are derived in this work. In addition, formula representations for the [xi]-index and the [xi]- function are obtained and the concept of the [xi]-index is related to that of the spectrum distribution function for some random operators.

eng

dc.identifier.merlin

b60063233

eng

dc.identifier.oclc

173847195

eng

dc.identifier.uri

https://hdl.handle.net/10355/4740

dc.identifier.uri

https://doi.org/10.32469/10355/4740

eng

dc.language

English

eng

dc.publisher

University of Missouri--Columbia

eng

dc.relation.ispartofcollection

University of Missouri--Columbia. Graduate School. Theses and Dissertations